{"id":"https://openalex.org/W3110977562","doi":"https://doi.org/10.3390/info11120580","title":"A Model for the Frequency Distribution of Multi-Scale Phenomena","display_name":"A Model for the Frequency Distribution of Multi-Scale Phenomena","publication_year":2020,"publication_date":"2020-12-13","ids":{"openalex":"https://openalex.org/W3110977562","doi":"https://doi.org/10.3390/info11120580","mag":"3110977562"},"language":"en","primary_location":{"id":"doi:10.3390/info11120580","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11120580","pdf_url":null,"source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/info11120580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062916710","display_name":"Paola Favati","orcid":"https://orcid.org/0000-0003-0382-3195"},"institutions":[{"id":"https://openalex.org/I4210130157","display_name":"Institute of Informatics and Telematics","ror":"https://ror.org/02gdcn153","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210130157","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola Favati","raw_affiliation_strings":["Istituto di Informatica e Telematica (IIT\u2013CNR), Via G. Moruzzi 1, 56124 Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0382-3195","affiliations":[{"raw_affiliation_string":"Istituto di Informatica e Telematica (IIT\u2013CNR), Via G. Moruzzi 1, 56124 Pisa, Italy","institution_ids":["https://openalex.org/I4210130157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027300466","display_name":"G. Lotti","orcid":"https://orcid.org/0000-0002-3299-1967"},"institutions":[{"id":"https://openalex.org/I124601658","display_name":"University of Parma","ror":"https://ror.org/02k7wn190","country_code":"IT","type":"education","lineage":["https://openalex.org/I124601658"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Grazia Lotti","raw_affiliation_strings":["Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, University of Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy","institution_ids":["https://openalex.org/I124601658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008473020","display_name":"O. Menchi","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ornella Menchi","raw_affiliation_strings":["Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022387101","display_name":"Francesco Romani","orcid":"https://orcid.org/0000-0001-8890-4490"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Romani","raw_affiliation_strings":["Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8890-4490","affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, University of Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062916710"],"corresponding_institution_ids":["https://openalex.org/I4210130157"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13861978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"12","first_page":"580","last_page":"580"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9666000008583069,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5971243381500244},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5667746067047119},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5502817034721375},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5058188438415527},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.5038115382194519},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4912514090538025},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.47550755739212036},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4728941023349762},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.46367523074150085},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4443749785423279},{"id":"https://openalex.org/keywords/frequency-distribution","display_name":"Frequency distribution","score":0.4386478066444397},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.4171158969402313},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.41365480422973633},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3889022171497345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3694416880607605},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3478369116783142},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20649704337120056},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1782589852809906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13456609845161438},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11337071657180786}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5971243381500244},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5667746067047119},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5502817034721375},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5058188438415527},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.5038115382194519},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4912514090538025},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.47550755739212036},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4728941023349762},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.46367523074150085},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4443749785423279},{"id":"https://openalex.org/C51921466","wikidata":"https://www.wikidata.org/wiki/Q1627586","display_name":"Frequency distribution","level":2,"score":0.4386478066444397},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.4171158969402313},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.41365480422973633},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3889022171497345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3694416880607605},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3478369116783142},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20649704337120056},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1782589852809906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13456609845161438},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11337071657180786},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/info11120580","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11120580","pdf_url":null,"source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1076370","is_oa":true,"landing_page_url":"https://www.mdpi.com/2078-2489/11/12/580","pdf_url":"https://www.mdpi.com/2078-2489/11/12/580/pdf?version=1608599205","source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e83ae8f099ac4097b1ce3e3ae972ea95","is_oa":true,"landing_page_url":"https://doaj.org/article/e83ae8f099ac4097b1ce3e3ae972ea95","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information, Vol 11, Iss 12, p 580 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2078-2489/11/12/580/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/info11120580","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Information; Volume 11; Issue 12; Pages: 580","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/info11120580","is_oa":true,"landing_page_url":"https://doi.org/10.3390/info11120580","pdf_url":null,"source":{"id":"https://openalex.org/S4210219776","display_name":"Information","issn_l":"2078-2489","issn":["2078-2489"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1568371145","https://openalex.org/W1953975752","https://openalex.org/W1993803315","https://openalex.org/W1994727615","https://openalex.org/W2000273502","https://openalex.org/W2036671379","https://openalex.org/W2082773934","https://openalex.org/W2101196063","https://openalex.org/W2109737807","https://openalex.org/W2118009636","https://openalex.org/W2122739512","https://openalex.org/W2134121682","https://openalex.org/W2136891251","https://openalex.org/W2155912844","https://openalex.org/W2258998514","https://openalex.org/W2889520008","https://openalex.org/W2949093975","https://openalex.org/W2963730104","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2330703564","https://openalex.org/W4302408253","https://openalex.org/W4233437273","https://openalex.org/W2347410987","https://openalex.org/W1990266565","https://openalex.org/W2032732601","https://openalex.org/W1573257936","https://openalex.org/W4391260377","https://openalex.org/W1963677898","https://openalex.org/W2123011400"],"abstract_inverted_index":{"Frequency":[0],"analysis":[1],"is":[2,80],"often":[3],"used":[4],"to":[5,39,89],"investigate":[6],"the":[7,70,73,77,94,98,105,108,113,120,142],"structure":[8],"of":[9,97,104,119,132,144],"systems":[10],"representing":[11],"multi-scale":[12],"real-world":[13],"phenomena.":[14],"In":[15,49],"many":[16,31,64],"different":[17],"environments,":[18],"functional":[19],"relationships":[20],"characterized":[21],"by":[22],"a":[23,54,60,83,90,130],"power":[24],"law":[25],"have":[26,46],"been":[27,47],"recognized,":[28],"but,":[29],"in":[30,67,129,137,141],"cases":[32],"this":[33,50],"simple":[34],"model":[35,57],"has":[36],"turned":[37],"out":[38],"be":[40],"absolutely":[41],"inadequate":[42],"and":[43,76,127],"other":[44],"models":[45,65],"proposed.":[48],"paper,":[51],"we":[52],"propose":[53],"general":[55,121],"abstract":[56],"which":[58,87,111],"constitutes":[59],"unifying":[61],"framework,":[62],"including":[63],"found":[66],"literature,":[68],"like":[69],"mixed":[71],"model,":[72,122],"exponential":[74],"cut-off":[75],"log-normal.":[78],"It":[79],"based":[81],"on":[82],"discrete-time":[84],"stochastic":[85],"process,":[86],"leads":[88],"recurrence":[91],"relation":[92],"describing":[93],"temporal":[95],"evolution":[96],"system.":[99],"The":[100],"steady":[101],"state":[102],"solution":[103],"system":[106],"highlights":[107],"probability":[109],"distribution,":[110],"underlies":[112],"frequency":[114],"behavior.":[115],"A":[116],"particular":[117],"instance":[118],"called":[123],"cubic-cut-off,":[124],"was":[125],"analyzed":[126],"tested":[128],"number":[131],"experiments,":[133],"producing":[134],"good":[135],"answers":[136],"difficult":[138],"cases,":[139],"even":[140],"presence":[143],"peculiar":[145],"behaviors.":[146]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2020-12-21T00:00:00"}
